Puppy Training?

I have a 14-week-old Westie puppy. During the past week or so everytime I bring her outside she runs from me; I think she’s being playful.
She’ll run a certain distance from me, and then lay down, then I’ll go to pick her up and she just keeps running from me. People have told me to flip her on her back when she acts up to get her to obey but I can’t catch her to do that. I can run faster than her, but shes so small it’s hard to catch her.
Just now she had to go out (it’s 3am, she usually needs to go out at this time everynight) and even though she was half asleep I just spend 15 minutes (no less) chasing her around the yard and I’m ready to kick the livin crap out of her.
I’ve considered putting her on a leash everytime I bring her outside and I guess that would be the obvious solution, but I feel like it would take to long to leash her everytime she has to go out since shes a puppy, she can’t hold very long. and she always bites the leash so it’s pointless.
any ideas?